The boom in natural-gas production has hit a new pressure point: The U.S. is running out of storage space.

Gas output has reached record levels in recent months, thanks in large part to the expansion of shale-gas fields. And the warm U.S. winter has reduced the amount of gas needed to heat homes and offices. That has filled storage facilities—often underground salt caverns or depleted oil and gas fields—to 57.8% capacity.

Gas producers, though, have plenty of reasons to keep the valves open. For one, they have spent billions of dollars investing in new production. And, in many fields, the cost of production is still lower than prices, analysts say.

"If gas went to zero, you'd still see drilling" in certain parts of the country, said Adam Bedard, senior director at consultancy Bentek Energy.